1. Field of the Invention
The present invention relates to a multipath eliminating filter, and particularly to a multipath eliminating filter which eliminates a multipath component arising at reception of an FM modulated signal or a phase modulated signal using an adaptive filter having variable filter characteristics.
2 Description of Prior Art
When an FM modulated signal or a phase modulated signal is to be received and demodulated, it is known that multipath transmission (multipath), where an undesirable reflected wave component caused by a building, mountain or the like is superimposed on a direct wave component, takes place, causing a deterioration in quality of reception such as an increase in distortion of a demodulated signal and the like. For a stationary receiver, this problem can be coped with by sharpening directivity of an antenna for tuning in to a direct wave. This measure, however, is not applicable to a mobile receiver. Thus, for a mobile receiver, it is proposed that an adaptive filter is used as a method of eliminating multipath distortion. This method utilizes a property that an amplitude (envelope) of an FM modulated signal is fixed. A digital filter is inserted at an intermediate frequency stage preceding an amplifier limiter, thereby varying filter characteristics so that an output amplitude of the digital filter is fixed.
FIG. 17 shows an example of a conventional multipath eliminating adaptive filter. The filter of FIG. 17 comprises an FIR filter having sufficient degree as described in literature 1 below, for example.
Literature 1: J. R. Treichler, B. G. Agee: "A New Approach to Multipath Correction of constant Modulus Signals", IEEEE Trans. vol. ASSP-31, No. 2, pp 459-471 (1983)
In FIG. 17, a digital signal of an A/D converted intermediate frequency signal is inputted to input terminal IN. With a value at time n of the input digital signal taken as x.sub.n, degree of an FIR (Finite Impulse Response) filter 1 as N, coefficient of the FIR filter 1 as c.sub.k (k=0 to N), and a value at time n of an output digital signal to be outputted to output terminal OUT as Y.sub.n, Y.sub.n is expressed by ##EQU1## Its matrix representation is EQU y.sub.n =C.sup.T X
where C.sup.T =[C.sub.0, C.sub.1, C.sub.2, . . . , C.sub.N ], X.sup.T =[x.sub.n, x.sub.n-1, x.sub.n-2, . . . , x.sub.n-N ], and the superscript ".sup.T " represents a transposed matrix.
With a reference amplitude value taken as 1, error .epsilon..sub.n is expressed by EQU .epsilon..sub.n =.linevert split.y.sub.n .linevert split..sup.2 -1
In an adaptive algorithm, evaluating function F is expressed by EQU F=E[.epsilon..sub.n.sup.2 ]
where E [*] indicates an expected value arithmetic.
Removal of multipath distortion is synonymous with minimization of F. Filter coefficient c.sub.k for minimizing F is determined by a steepest gradient of F. Hence, update filter coefficient c.sub.k as follows, for use at next time (n+1). EQU c.sub.k .rarw.c.sub.k -.alpha.(.differential.F/.differential.c.sub.k)
where .alpha. is a fixed convergence parameter.
In the example of FIG. 17, an operator 2 squares an absolute value of Y.sub.n, and a subtracter 3 subtracts a reference amplitude value of 1 from the absolute value squared to obtain .epsilon..sub.n. A filter update unit 4 performs an expected value arithmetic and an update calculation on a filter coefficient. Thus, an updated filter coefficient is set for the FIR filter 1.
FIG. 18 shows another example of a multipath eliminating adaptive filter. The filter of FIG. 18 comprises an FIR filter having a nonzero filter coefficient only at points corresponding to integer multiples of a delay time of a reflected wave. Furthermore, a multiplier for level adjustment is provided on the subsequent stage side of the FIR filter for normalizing an amplitude of a direct wave to 1. It is described in literature 3 below as an improved version of an invention disclosed in literature 2.
Literature 2: Japanese Patent Application Laid-open No. 140527/1987
Literature 3: Japanese Patent Application Laid-open No. 62628/1991
When one reflected wave is involved and when a reflection coefficient at normalization by a direct wave is taken as r and a delay time of the reflected wave as t, transfer function H.sub.MP of multipath is represented by EQU H.sub.MP (z)=1+rz.sup.-t
Transfer function H.sub.EQ to be realized by the multipath eliminating adaptive filter is an inverse function of H.sub.MP as represented by ##EQU2##
Thus, H.sub.EQ is realized at an FIR filter 5 by selecting an appropriate L.
In the example of FIG. 18, after squaring an absolute value of output y.sub.n from the FIR filter 5 at an operator 6, the absolute value squared is multiplied by a variable gain coefficient g at a level adjusting multiplier 7 for normalizing an amplitude of a direct wave to 1.
In this case, evaluating function F in an adaptive algorithm is expressed by ##EQU3##
A subtracter 8 subtracts 1 from an output of the multiplier 7 to obtain error .epsilon..sub.n and outputs it to a filter update unit 9.
Update expressions for updating r, t, and g by a method of steepest gradient are EQU r.rarw.r-.alpha..sub.1 (.differential.F/.differential.r) EQU t.rarw.t-.alpha..sub.2 (.differential.F/.differential.t) EQU g.rarw.g-.alpha..sub.3 (.differential.F/.differential.g)
where .alpha..sub.1 -.alpha..sub.3 are fixed convergence parameters.
The filter update unit 9 performs an expected value arithmetic and an update calculation on r, t, and g. Thus, updated filter characteristics r and t are set for the FIR filter 5, and an updated gain coefficient g is set for the multiplier 7.
If a unit delay time (here, a sampling period for a digital signal) u of a delay element of the FIR filter 5 is fixed and is far smaller than t, filter coefficient c.sub.k is obtained from r and t by the following expressions: EQU c.sub.k =(-r).sup.p k=p EQU c.sub.k =0 k.noteq.p
The obtained c.sub.k is set for the FIR filter 5 as an update filter coefficient. p=[vt/u] (v is a variable assuming an integer greater than 0), and a maximum integer not exceeding vt/u.